Details

sample66.0ms

Algorithm

intervals

Results

29.0ms	78×	body	1280	valid
12.0ms	49×	body	640	valid
7.0ms	178×	body	80	valid
4.0ms	25×	body	320	valid
1.0ms	13×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
3	15
2	13
1	10
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.6b	(- (exp x) 1.0)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 68

Calls

2 calls:

27.0ms	(/ (- (exp x) 1.0) x)
30.0ms	(- (exp x) 1.0)

series56.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify888.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1006
1	296
0	127

prune377.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (* x x) x) x)
0.1b	(* (* x x) x)
3.5b	(/ (fma (* x x) 1/2 (fma 1/6 (* (* x x) x) x)) x)
11.6b	(fma (* x x) 1/2 (fma 1/6 (* (* x x) x) x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
6×	`pow-plus` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-l` `pow3` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma 1/6 (* (* x x) x) x)
14.0ms	(* (* x x) x)
4.0ms	(/ (fma (* x x) 1/2 (fma 1/6 (* (* x x) x) x)) x)
0.0ms	(fma (* x x) 1/2 (fma 1/6 (* (* x x) x) x))

series239.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(fma 1/6 (* (* x x) x) x)
43.0ms	(* (* x x) x)
57.0ms	(/ (fma (* x x) 1/2 (fma 1/6 (* (* x x) x) x)) x)
40.0ms	(fma (* x x) 1/2 (fma 1/6 (* (* x x) x) x))

simplify1.4s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1344
1	224
0	106

prune478.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
3.2b	(- (/ (exp x) x) (/ 1.0 x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

262×	`times-frac`
213×	`add-sqr-sqrt`
209×	`*-un-lft-identity`
201×	`add-cube-cbrt`
169×	`prod-diff`
30×	`div-inv`
13×	`fma-neg`
4×	`add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `add-exp-log` `associate-/l`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `distribute-rgt-out--` `diff-log` `div-exp` `frac-sub` `flip--` `sub-div`

Counts

2 → 236

Calls

2 calls:

11.0ms	(/ (exp x) x)
61.0ms	(- (/ (exp x) x) (/ 1.0 x))

series91.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) x)
63.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify1.9s

Counts

242 → 242

Iterations

Iter	Nodes
done	5001
2	2598
1	783
0	342

prune882.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (exp x) x) (/ (exp x) x))
0.2b	(* (/ 1.0 x) (/ 1.0 x))
10.5b	(/ (- (* (/ (exp x) x) (/ (exp x) x)) (* (/ 1.0 x) (/ 1.0 x))) (+ (/ (exp x) x) (/ 1.0 x)))
25.8b	(- (* (/ (exp x) x) (/ (exp x) x)) (* (/ 1.0 x) (/ 1.0 x)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

142×	`times-frac`
124×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
30×	`add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
22×	`associate-l/` `associate-r/`
20×	`distribute-lft-out`
19×	`div-inv`
18×	`frac-times` `pow1` `frac-sub`
16×	`associate-/l/`
10×	`sub-div` `difference-of-squares`
9×	`cbrt-undiv` `div-exp`
8×	`associate-/r*` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp`
5×	`distribute-rgt-out`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r/`
2×	`pow2` `pow-plus` `flip3--` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `prod-diff` `frac-add` `flip-+`

Counts

4 → 247

Calls

4 calls:

34.0ms	(* (/ (exp x) x) (/ (exp x) x))
18.0ms	(* (/ 1.0 x) (/ 1.0 x))
81.0ms	(/ (- (* (/ (exp x) x) (/ (exp x) x)) (* (/ 1.0 x) (/ 1.0 x))) (+ (/ (exp x) x) (/ 1.0 x)))
17.0ms	(- (* (/ (exp x) x) (/ (exp x) x)) (* (/ 1.0 x) (/ 1.0 x)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ (exp x) x) (/ (exp x) x))
55.0ms	(* (/ 1.0 x) (/ 1.0 x))
205.0ms	(/ (- (* (/ (exp x) x) (/ (exp x) x)) (* (/ 1.0 x) (/ 1.0 x))) (+ (/ (exp x) x) (/ 1.0 x)))
130.0ms	(- (* (/ (exp x) x) (/ (exp x) x)) (* (/ 1.0 x) (/ 1.0 x)))

simplify1.3s

Counts

259 → 259

Iterations

Iter	Nodes
done	5001
1	1314
0	372

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes48.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 20.7b

bsearch39.0ms

Steps

Iters	Range		Point
9	-0.042530208599811804	-3.2052418334402957e-07	-0.0001629133836907385

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	16

end0.0ms

sample2.1s

Algorithm

intervals

Results

745.0ms	2280×	body	1280	valid
526.0ms	860×	body	320	valid
379.0ms	1687×	body	640	valid
186.0ms	5375×	body	80	valid
33.0ms	435×	body	160	valid